15. A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 6 feet above the bow. The rope is hauled in at the rate of 2 ft. /sec Ring at edge of dock How fast is the boat approaching the dock when 10 feet of rope are out? а. b. At what rate (rads/min) is the angle 0 changing then?

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A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the​ house, the base is moving away at the rate of 24 ​ft/sec. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​then? c. At what rate is the angle between the ladder and the ground changing​ then? A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta. θ x(t)y(t)010-ft ladderxy   a. The rate of change of the height of the top of the ladder is nothing ​ft/sec. ​(Simplify your​ answer.)   b. The area is changing at…

A 5 metre long ladder is leaning against a vertical wall, with its foot on horizontal ground. The foot of the ladder slides away from the wall at a rate of 2ms1. At what rate is the angle between the ladder and the ground decreasing when the foot of the ladder is 4 metres from the wall? Select one: rad s-1 O - rad s1 O 6 rad s-1 O - rad s1